Review on multicritical phase transitions

Leone V. Luzzatto, Juan Felipe Barrera López, István A. Kovács

The contact process is a simple infection spreading model showcasing an out-of-equilibrium phase transition between a macroscopically active and an inactive phase. Such absorbing state phase transitions are often sensitive to the presence of quenched disorder. Traditionally, a phase transition in the disordered contact process is either triggered by dilution or by locally varying the infection rate. However, when both factors play an important role, a multicritical point emerges that remains poorly understood. Here, we study the multicritical contact process by large-scale Monte Carlo simulations in two and three dimensions. The multicritical behavior is found to be universal and exhibits ultra-slow, activated dynamical scaling, with exponents consistent with those predicted by the strong disorder renormalization group method. This finding indicates that the multicritical contact process belongs to the same universality class as the multicritical quantum Ising model, in both two and three dimensions.

David A. Lavis, Roman Frigg

David R. Nelson

Recent theoretical work has led to closed form expressions for the thermodynamic functions which characterize complicated multricritcal phenomeana. Renormalization group recursion relations are used to map multicritical systems out of the critical regime, at which point Landau theory with fluctuation corrections can be employed. We review here applications of this approach to tricritical points, spin flop transitions, dipolar systems, and Heisenberg ferromagnets below Tc. Although the calculations have presently been carried out only to first order ε=4−d, they nevertheless give a good qualtiative understanding of multicritical behavior. In particular, they provide a detailed picture of the crossover between competing kinds of critical behavior, and allow treatment of ordered phases with spontaneously broken symmetries.

Jia-Xin Wang, Qian Bin, Jing-Jing Cao +1 more

Precise control of criticality in superradiant phase transitions is essential for quantum state engineering and the simulation of nonequilibrium phase transitions. Here, we investigate theoretically multicritical phenomena in a dissipative two-Rydberg-atom cavity--QED system. The intrinisic dipole--dipole interaction between the two Rydberg atoms restructures the energy-level landscape of the atomic subsystem, thereby significantly modifying the boundary of the continuous second-order superradiant phase transition, and shifting both the phase boundary and the multicritical point toward weaker atom--cavity strengths. For sufficiently strong dipole--dipole interactions, the continuous second-order phase transition and the multicritical point both disappear, leaving only a discontinuous first--order phase transition that enables the emergence of a superradiant phase even at arbitrarily weak atom--cavity coupling. This work is of fundamental interest for studying dissipative quantum phase transitions, with potential implications for quantum precision measurement and quantum sensing.